Quantifying gender imbalance in East Asian academia: Research career and citation practice

Gender imbalance in academia has been confirmed in terms of a variety of indicators, and its magnitude often varies from country to country. Europe and North America, which cover a large fraction of research workforce in the world, have been the main geographical regions for research on gender imbalance in academia. However, the academia in East Asia, which accounts for a substantial fraction of research, may be exposed to strong gender imbalance because Asia has been facing persistent and stronger gender imbalance in society at large than Europe and North America. Here we use publication data between 1950 and 2020 to analyze gender imbalance in academia in China, Japan, and South Korea in terms of the number of researchers, their career, and citation practice. We found that, compared to the average of the other countries, gender imbalance is larger in these three East Asian countries in terms of the number of researchers and their citation practice and additionally in Japan in terms of research career. Moreover, we found that Japan has been exposed to the larger gender imbalance than China and South Korea in terms of research career and citation practice.


Introduction
Author-name disambiguation is a challenging problem in bibliographic data analysis 24 .Like the MAG, the OpenAlex uses a proprietary algorithm to identify and assign a unique ID to each author using their name, publication record, citation patterns, and if available, Open Researcher and Contributor ID (ORCID) 51 .The OpenAlex's author-name disambiguation algorithm identified 40,134,800 authors.We assigned one of the 19 research disciplines to each of the 37,921,048 authors (94.5%) based on their papers; we assigned no discipline to the other authors (see Supplementary Section S1 for the assignment method).We also assigned a country to each author based on the country code (i.e., the ISO two-letter country code) associated with their institutions (see Supplementary Section S2 for the assignment method).As a result, 7,684,496 authors were affiliated with an institution in China, 2,103,087 authors in Japan, 784,120 authors in South Korea, and 29,563,097 authors in other countries.It should be noted that this country assignment is distinct from the author's country of origin, their ethnicity, or the language that their name is from.

Separating first and last names
We use the first name to infer an author's gender.However, the author's name is not explicitly separated into the first and last names in the OpenAlex data.Therefore, we enumerated candidates of their first and last names as follows.First, we excluded the 112,763 authors (0.3%) with a one-word name, which is presumably due to error in the original data.Then, because different words in the author's name are separated by space (e.g., John Smith), we regarded that the last name is the last space-separated word.For example, the last name of "John Smith" is Smith according to our procedure.
Next, we acquired the candidates of the first name for the authors in China, Japan, or South Korea (i.e., those for whom we estimated the country to be China, Japan, or South Korea from their affiliations) as follows.Chinese or Japanese names written in English typically consist of two words separated by space (e.g., Meiling Jiang or Hitomi Yamada).In South Korean names, the first two or more space-separated words may be their first name.For example, "Gil Dong" may be the first name of the name "Gil Dong Hong".Therefore, if the author is in China, Japan, or South Korea and their name consists of k space-separated words, denoted by w 1 , w 2 , . . ., w k , then we use w 1 , w 1 w 2 , . .., and w 1 • • • w k−1 as k − 1 candidates of their first name.For example, the unique candidate of the first name for the name "Gildong Hong" is "Gildong".In contrast, the candidates of the first name for the name "Gil Dong Hong" are "Gil" and "Gil Dong".
For the rest of the authors, i.e., those who reside in countries other than China, Japan, and South Korea, we assume that the first space-separated word of their name is their first name.

Gender of authors
We infer an author's gender using an application programming interface (API) named the Gender API 4 .The database constituting Gender API contains over six million unique names across 191 countries 4 .Gender API has been deployed in previous studies that investigated gender imbalance in academia 18,20,54,56 .Furthermore, its accuracy for Asian names is superior to competing services on a benchmark data set 52 .
We constructed the gender assignment methods that yield at least 90% classification accuracy on the small set of samples with the ground truth, which we call the test set, as follows.First, when one inputs a first-name candidate to Gender API, it returns either "female", "male", or "unknown", its 'accuracy' (which is a terminology of Gender API and different from the classification accuracy on the test set discussed below; therefore we put the quotation marks here and in the following text), and the number of samples of the provided first name in the database.Second, for the authors in either China, Japan, or South Korea, we decided to feed their country, which is an optional input to the API, in addition to each candidate of their first name.In contrast, for the authors in the other countries, we fed each candidate of their first name to the API without specifying their country.We used the country in some cases and not others because the classification accuracy on the test set was higher in this way.Note that we assessed the classification accuracy of any gender assignment method by manually checking the correctness of the assigned gender on the test set (see Supplementary Section S3 for the details).Third, we discarded the API's output when the 'accuracy' that the API returned was smaller than θ or the number of samples was smaller than n s .We then identified the largest 'accuracy' value among all the input first-name candidates that returned female as output.Similarly, we identified the largest 'accuracy' value among all the input first-name candidates that returned male as output.If the former was larger than the latter, we assigned female to the author.If the former was smaller than the latter, we assigned male to the author.If the former was equal to the latter, then we did not assign female or male to the author.
We set the θ and n s values depending on a given author's country and first publication year.Specifically, for the authors in China, we set θ = 90% and n s = 10 if their first publication year, denoted by y, is 1990 or before; θ = 99% and n s = 10 if 1991 ≤ y ≤ 2000; θ = 99% and n s = 50 if 2001 ≤ y ≤ 2010; θ = 95% and n s = 10 if 2011 ≤ y ≤ 2020.For the authors in Japan, we set θ = 99% and n s = 10 if y ≤ 1990, and θ = 90% and n s = 10 if 1991 ≤ y ≤ 2020.For the authors in the other countries including South Korea, we set θ = 90% and n s = 10 for any y.With this choice, the classification accuracy on the test set is at least 90% for each pair of the country (i.e., China, Japan, South Korea, and the other countries) and the year group (i.e., (i) y ≤ 1990, (ii) 1991 ≤ y ≤ 2000, (iii) 2001 ≤ y ≤ 2010, and (iv) 2011 ≤ y ≤ 2020).
In this manner, we assigned a binary gender to 18,002,917 (with 6,485,368 females) out of the 40,134,800 authors, with 387,925 authors (with 89,838 females) in China, 1,267,205 authors (with 216,579 females) in Japan, 342,452 authors (with 44,257 females) in South Korea, and 16,005,335 authors (with 6,134,694 females) in the other countries.The authors in the top 31 countries in terms of the number of gender-assigned authors combined account for 90.0% of those in the other countries.In descending order in terms of the number of gender-assigned authors, these countries are US, UK, Germany, Brazil, France, India, Canada, Spain, Italy, Australia, Islamic Republic of Iran, Netherlands, Switzerland, Mexico, Russian Federation, Poland, Turkey, Sweden, Indonesia, Belgium, Egypt, Colombia, Israel, Denmark, Austria, Pakistan, Czechia, Greece, Argentina, Finland, and Malaysia.

Nationality of authors
A Japanese author and a foreign author in Japan may be subject to different degrees of gender imbalance.To examine this possibility, we used an API named Nationalize.io 6to infer the nationality of the authors in China, Japan, or South Korea.For a given first or last name, Nationalize.ioreturns the candidates of the nationality of the person and their probabilities.The database constituting Nationalize.iocontains approximately 114 million names across many countries.
For each author u, we ran Nationalize.ioseparately with u's last name as input and with each candidate of u's first name as input.For each input, Nationalize.ioreturned up to five nationality candidates with the largest probabilities.Denote by c the country in which u resides (i.e., China, Japan, or South Korea).If Nationalize.iooutputs c as a candidate of u's nationality and its probability is at least 0.9 for at least one candidate of u's first name or u's last name, we set c as u's nationality and therefore regard that u is a native author (i.e., those who work in the country where they have nationality) in country c.In contrast, we regard that u is a non-native author if the probability of country c is not greater than 0.1 for all candidates of u's first name and u's last name.Specifically, we do so if at least one of the following three criteria is met for each of the author's name words as input: (i) Nationalize.iooutputs c as a candidate of the nationality and its probability is 0.1 or smaller; (ii) Nationalize.iodoes not output c as a candidate of the nationality, and the smallest probability of the country in the output of Nationalize.io is at most 0.1, or (iii) Nationalize.iodoes not output c as a candidate, and the sum of the probabilities associated with all the output countries is at least 0.9.Note that, if criterion (ii) or (iii) is met, then the probability of nationality c is at most 0.1 because the API returns up to five nationality candidates with the largest probabilities.Otherwise, we regarded the author to be neither native nor non-native to the country.
For example, if the author's name is "Hitomi Yamada", we separately input "Hitomi" and "Yamada" to Nationalize.io.Suppose that Nationalize.ioreturns the following nationalities and their probabilities: {(Japan, 0.80), (China, 0.05)} for "Hitomi" and {(Japan, 0.91), (Thailand, 0.02), (Vietnam, 0.01)} for "Yamada".If the author is in Japan, we regard that the author is a Japanese native because the probability of Japan given "Yamada" is larger than 0.9.In contrast, if Hitomi Yamada is in China, we regard that the author is non-native because the output for the input name "Hitomi" satisfies criterion (i) and that for the input name "Yamada" satisfies criteria (ii) and (iii).
Among the gender-assigned authors, we found 131,372 native and 13,700 non-native authors in China, 1,179,036 native and 17,030 non-native authors in Japan, and 200,325 native and 6,338 non-native authors in South Korea.Note that many authors are not assigned to be native or non-native.

Characterizing gender imbalance in research career
We characterize the career of author u using the five indicators proposed in Ref. 30 : (i) total productivity defined as the number of papers authored by u; (ii) total impact defined as the sum of the citation impact across papers authored by u (see Supplementary Section S4 for the definition of citation impact of a paper); (iii) career length defined as the difference between the publication dates of the first and last papers authored by u, which we divide by 365; (iv) annual productivity defined as the ratio of u's total productivity to u's career length; (v) number of coauthors defined by the number of authors that coauthored at least one paper with u.
For the combination of an indicator and a set of authors, we define the gender gap by (µ F − µ M )/µ M , where µ F and µ M denote the mean value of the indicator for the female and male authors in the set, respectively.A positive gender gap value implies that females have stronger careers than males in terms of the indicator used, and vice versa.

Characterizing gender imbalance in citation practice
We quantify gender imbalance in citation practice of authors in China, Japan, South Korea, and the other countries using the methods developed in Ref. 20 .We focus on citations between pairs of papers among the 27,616,941 papers for each of which both the first and last authors have the same gender and the same country, including the case of a country other than China, Japan, and South Korea.We denote by S the set of all the papers.We identify four categories, i.e., MM, MW, WM, and WW, based on the gender of the first and last authors, where the first letter, M or W, indicates that the first author is male (man) or female (woman), respectively, and the second letter indicates the gender of the last author.We classify single-author papers to the MM or WW category.
Consider two subsets of papers denoted by S from ⊆ S and S to ⊆ S. We measure the extent to which the papers in S from over-or under-cite the papers in S to and in a given gender category (i.e., MM, MW, WM, or WW).To this end, for each paper z ∈ S from , we focused on citations made by z to each paper z ∈ S to such that (i) the publication date of z is at most ten years older than that of z and (ii) both first and last authors of z are neither the first nor last author of z.The original method used all the citations made by z to any papers published before z to investigate gender imbalance in citation practice 20 .In contrast, a previous study adopted criterion (i) to measure gender imbalance in the research career 30 .We adopt criterion (i) because in this manner we can simultaneously examine gender imbalance in research career and citation practice with the same data.We impose criterion (ii) to avoid self-citations.We denote by S to (z) the set of the papers that meet criteria (i) and (ii) for a given paper z.
Given a gender category g ∈ {MM, MW, WM, WW}, we first count the citations made by each paper z ∈ S from to the papers in S to (z) and in gender category g, which we denote by n z→g,obs .Then, we compare ∑ z∈S from n z→g,obs with the expectation under the so-called random-draws model 20 .The random-draws model assumes that c z papers cited by paper z ∈ S from are drawn from S to (z) uniformly at random, where c z is the number of citations made by z to the papers in S to (z).Then, the expected number of citations that the papers in S to (z) and in gender category g receive from z under the random-draws model, denoted by n z→g,rand , is equal to c z p z,g , where p z,g is the fraction of the papers that are in both S to (z) and g.We sum n z→g,rand over z, which yields the expected number of citations received by the papers in both S to and g.Then, we calculate the over/under-citation of the papers that belong to both S to and g as (∑ z∈S from n z→g,obs − ∑ z∈S from n z→g,rand )/ ∑ z∈S from n z→g,rand .
Previous studies additionally deployed another reference model, called the relevant characteristics model, for calculating the expected number of citations 20 .We do not use this method because the Newton's method to determine the smoothing parameters does not sufficiently converge due to a huge number of papers.Therefore, the present study reports the over/under-citation obtained using the random-draws model.

Gender imbalance in research career
We first examine gender imbalance in the set of authors in China (i.e., their country of affiliation was estimated to be China), Japan, South Korea, and the other countries.We identified 7,684,496 authors in China, 2,103,087 authors in Japan, 784,120 authors in South Korea, and 29,563,097 authors in the other countries.In each country group, the number of authors has increased from 1990 to 2020, in particular in China (see Fig. 1(a)); by definition, we counted the authors who had published their first paper in each given year.Among these authors, we were able to assign a binary gender to 387,925 authors in China, 1,267,205 authors in Japan, 342,452 authors in South Korea, and 16,005,335 authors in the other countries.The fractions of female authors are 23.2%, 17.1%, and 12.9% in China, Japan, and South Korea, respectively.The ranking among the three East Asian countries in our data set is consistent with previous results 19,44 .These fractions are smaller than that for the other countries in our data set (i.e., 38.3%).As a reference, the fraction for 83 countries excluding China, Japan, and South Korea was 28.5% in a previous study 30 .The fraction of female authors is the highest in psychology and the lowest in engineering among the 19 disciplines in the three East Asian countries, whereas it is the highest in sociology and the lowest in physics in the other countries (see Supplementary Section S5 for details).The fraction of female authors has increased over the three decades in each country group (see Fig. 1(b)).Specifically, while female authors represented 16.4%, 6.4%, 3.4%, and 28.2% in China, Japan, South Korea, and the other countries, respectively, in 1990, the fraction increased to 24.8%, 22.2%, 19.5%, and 45.4% in 2020.The fractions for China, Japan, and South Korea have been smaller than that for the other countries over the three decades (see Fig. 1(b)).
We now compare gender imbalance in the research career among different countries.In the remainder of this subsection, we focus on the gender-assigned authors in each country group (i.e., China, Japan, South Korea, or the other countries) who meet the following criteria: (i) they publish at least two papers, (ii) the difference between the publication dates of their first and last papers is more than 365 days, (iii) they publish fewer than 20 papers per year on average, and (iv) their last publication date is on or before December 31st, 2015.Criteria (i)-(iii) are the same as those employed in Ref. 30 .We extended the year of the last publication in criterion (iv) from 2010, which was used in Ref. 30 given that the last year that their data set covered was 2016, to 2015 given that the last year that our data set covers is 2020.There are 17,813 such authors (with 20.3% being females) in China, 327,946 (14.0%females) in Japan, 57,466 (9.8% females) in South Korea, and 2,544,059 (33.4% females) in the other countries.
We have found that the authors in Japan are exposed to a notably larger gender gap in terms of the total productivity than those in "the other countries" group, whose gender gap is larger than those in China and South Korea (see the bars labeled "Overall" in Fig. 2(a)).These results persist when we compare the top 20% female authors and the top 20% male authors in each country group (see the bars labeled "Top 20%" in Fig. 2(a)).When we compare the middle 20% females and the middle 20% males in each country group, the gender gap is almost eliminated for China and South Korea but remained for Japan and the other countries (see the bars labeled "Middle 20%" in Fig. 2(a)).Last, there is no gender gap between the bottom 20% females and the bottom 20% males in each country group (see the bars labeled "Low 20%" in Fig. 2  and South Korea including the magnification of the gender gap in the "Top 20%" authors and its suppression in the middle and bottom groups of authors are similar to those in a recent study analyzing 83 countries although that study excluded China, Japan, and South Korea 30 .In terms of the total impact of an author, we have observed qualitatively different results (see Fig. 2(b)).Female authors receive more citations than male authors on average in China and South Korea and vice versa in Japan and the other countries.These results remain qualitatively the same when we compare the top 20% females and the top 20% males in each country group.In contrast, in the comparison between the middle 20% females and the middle 20% males, and between the bottom 20% females and the bottom 20% males, the females receive more citations than the males in each country group.Our results for China and South Korea are different from the previous results 30 in that the overall and top 20% females receive more citations than the males in China and South Korea in ours.Our results for Japan and the other countries are consistent with the previous results 30 .
For further investigation of the gender gap in total productivity, we decompose the total productivity of each author into the product of their annual productivity and career length 30 ; the career length is defined as the difference between the first and last publication dates.We have found a small gender gap in the annual productivity of the authors in each country group (see Fig. 2(c)).The gender gap remains small in the comparison between the top 20% females and the top 20% males in each country group as well.These results are consistent with the previous results 30 .
The lack of gender gap in annual productivity in each country group suggests that the country-to-country difference in the gender gap in total productivity may be ascribed to that in career length.As expected, the gender gap in the career length is present in each country group both when we compare all females and males and when we compare the top 20% authors of each gender (see Fig. 2(d)).The gender gap in the career length is the strongest in Japan, then "the other countries" group, South Korea, and the weakest in China.This result is also expected because the annual productivity is roughly free of the gender gap and the gender gap in the total productivity is also the strongest in Japan, then "the other countries" group, South Korea, and the weakest in China.The presence of a gender gap in career length for the overall and top 20% authors by gender in each country group is consistent with the previous results 30 .
To sum up, we found that the gender gaps in terms of the four indicators in each country group are overall similar to the previous results 30 and that these gender gaps are the largest in Japan, then "the other countries" group, South Korea, and weakest in China.
Gender imbalance may be different between native and non-native authors in a country.For example, Chinese authors working in China and foreign authors working in China may be exposed to different levels of gender imbalance.Therefore, we compare gender imbalance between "native" authors and "non-native" authors in China, Japan, and South Korea.There are 4,915 natives (with 20.7% females) and 974 non-natives (with 25.6% females) in China; 311,550 natives (with 13.2% females) and 2,858 non-natives (with 19.0% females) in Japan; and 32,144 natives (with 13.0% females) and 666 non-natives (with 17.7% females) in South Korea.We compare the four indices of gender gap between native and non-native authors in China, Japan, and South Korea in Fig. 3(a).The figure suggests that non-native females tend to be at more disadvantage than native females in China.In contrast, in Japan, native females tend to be at more disadvantage in terms of research career than non-native females except in terms of annual productivity.The results for South Korea are, roughly speaking, intermediate between those for China and Japan.These results suggest that natives and non-natives perceive different gender imbalance and how they do so depends on countries even within East Asia.While we have been ignorant of the author's position, a previous study suggested that female authors are less likely to appear in the prominent author position (i.e., the first-or last-author position or sole author) 37,62 ; authors in these positions generally play main roles in the research and writing of the paper in many research disciplines.To investigate whether gender imbalance depends on the author position, we now restrict the set of papers for each author u to those in which u is in the prominent position.Then, using the restricted set of papers, we examine whether or not u meets the same four criteria for filtering the authors.Note that u may not satisfy the criteria after we restrict the papers in this manner even if u satisfies the same criteria based on the entire set of papers (e.g., u has written papers but never as prominent author).After removal of the authors that do not satisfy the four criteria as prominent author, there are 10,180 authors (with 15.4% females) for China, 185,874 authors (with 10.2% females) for Japan, 31,936 authors (with 8.3% females) for South Korea, and 1,825,707 authors (with 29.4% females) for the other countries.The gender gap qualitatively remains the same in each country group when one calculates the four indicators of research career only using the papers in which u is in the prominent position (see Fig. 3(b)).In other words, females publish fewer papers, receive more citations in China and South Korea but fewer citations in Japan and the other countries, and have shorter career lengths than males, and the annual productivity is similar between the females and males.Furthermore, female authors tend to be at more disadvantage in the prominent author position than in any author position in all the country groups, except in terms of the career length for China (see Fig. 3(b)).
Among our research performance indicators (i.e., total productivity, total impact, and annual productivity), we have observed gender imbalance in the total productivity and total impact.Prior research showed that gender imbalance in the career length 30 and that in the number of coauthors 39 explain most of the variance in the research performance.To test the existence of similar correlates in each country group, we carry out matching experiments 30,39 in which the gender gap in terms of the career length or number of coauthors is eliminated.We generate the three matched sets of authors as follows.For each female author, we select without replacement a male that has the same country group, the same year of the first publication, the same discipline, and the same career length in the case of the first matched set.For the second matched set, we impose that the matched male author has the same number of coauthors instead of the same career length as the female author.For the third matched set, we impose that the matched male author has both the same career length and the same number of coauthors.In these matching experiments, we do not use the authors to whom a research discipline has not been assigned.Then, we measure the gender imbalance within each set.
We have found that the gender gaps in both total productivity and total impact have drastically decreased after controlling for either the career length or the number of coauthors in all the country groups, except for total impact for China and South Korea (see Fig. 4).When we only use the papers in which the author is in the prominent position, the gender gaps have considerably decreased in the matching experiments in all the country groups (see Supplementary Section S6 for details).Therefore, consistent with the previous results 30,39 , both the career length and the number of coauthors seem to be key contributors to the gender imbalance in the total productivity and total impact of authors in East Asia as well as in other countries.Moreover, the gender gaps in total productivity and total impact little decrease after controlling for both the career length and the number of coauthors compared with controlling for just one of them.These results suggest that the author's career length and number of coauthors are correlated.In fact, the Pearson correlation coefficient between the career length and the number of coauthors of the authors is roughly 0.4 for each country group (see Supplementary Section S7 for details).

Gender imbalance in citation practice
The gender imbalance in research performance may owe not only to differences between females and males in their research career, such as the career length and the number of coauthors, but also those in citation practices 23,33,38 .Therefore, we compare gender imbalance in citation practice between authors in each country group in this section.We use the 27,616,941 papers each of which falls into four gender categories (i.e., MM, MW, WM, or WW) and has the first and last authors in the same country group (i.e., China, Japan, South Korea, or the other countries).Note that we regard sole-author papers by males and females as MM and WW papers, respectively.There are 66,569 papers (i.e., 53,918 MM, 2,451 MW, 3,945 WM, and 6,255 WW papers) available for this analysis from China, 1,741,061 papers (i.e., 1,547,977 MM, 38,199 MW, 130,235 WM, and 24,650 WW papers) from Japan, 248,388 papers (i.e., 212,509 MM, 6,507 MW, 23,999 WM, and 5,373 WW papers) from South Korea, and 25,560,923 papers (i.e., 16,240,956 MM, 2,000,691 MW, 3,546,901 WM, and 3,772,375 WW papers) from the other countries.
We now compare gender imbalance in citations made by authors in China, Japan, South Korea, and the other countries.We first count the number of citations made by any papers from each country group to any papers in each gender category (i.e., MM, MW, WM, and WW).Then, we compare the obtained citation counts with the expected numbers for the random-draws model, which assumes that each paper cites other papers uniformly at random.We have found that main patterns of over/under-citation of papers in each gender category is qualitatively the same in China, Japan, and South Korea; papers published in these countries over-cite MM and WM papers and under-cite WW papers (see Fig. 5(a)).The degree of these over/under-citations is weaker in China than in Japan and South Korea, and slightly larger in Japan than in South Korea (see Fig. 5(a)).Compared with the three East Asian countries, the papers published in the other countries cite less MM papers and more MW, WM, and WW papers (see Fig. 5(a)).Our results of the over-citation of MM papers, which is observed for China, Japan, and South Korea, and the under-citation of WW papers, which is observed for any country group, are consistent with those in previous studies that examined papers from different countries altogether 20,25,61 .
The amount of over/under-citation made by the papers in each gender category is qualitatively similar among China, Japan, South Korea, and the other countries, which we summarize as follows.First, the MM papers over-cite MM and WM papers and under-cite WW papers (see Fig. 5(b)).Second, the MW papers under-cite MM and WW papers and over-cite MW and WM papers (see Fig. 5(c)).The WM papers from each country group also show qualitatively the same citation practice (see Fig. 5(d)).Therefore, the MM, MW, and WM papers from each country group under-cite WW papers on average.Third, in contrast, the WW papers under-cite MM papers and over-cite MW, WM, and WW papers (see Fig. 5(e)).These results are consistent with the previous results for papers published from any countries on neuroscience in that MM, MW, and WM papers under-cite WW papers and that WW papers under-cite MM papers and over-cite WW papers 20,61 .Fourth, papers in any gender category of author tend to cite WM papers more than MW papers (see Figs. 5(b)-(e)).In sum, we observe consistent gender imbalance with which papers involving males in a prominent position tend to over-cite male papers, broadly defined, and papers in which the first and last authors are both females tend to over-cite female papers.
Figure 5 also reveals differences in over/under-citation behavior among the four country groups.First, in any gender category of author, papers from the three East Asian countries under-cite WW papers and over-cite MM papers more strongly than those in the other countries, except for the MM papers from China.Second, papers from the three East Asian countries under-cite MW and WM papers more strongly than in those in the other countries, while we do not have active interpretation of this result.Third, among the three East Asian countries, in any gender category of author, Japanese and South Korean papers under-cite WW papers more strongly than Chinese papers.
Citation practice is often subject to country bias.For example, health professionals in the US and UK tend to over-cite articles published in a medical journal of their own countries 17 ; in nanotechnology, Chinese authors are more likely to cite each other than US authors do 55 .Motivated by these previous findings, we hypothesize that papers from China, Japan, and South Korea cite papers from the same country in a different gender-biased manner compared to when citing papers from the other countries.To investigate this possibility, we decompose citations made by the papers from each country into domestic citations (i.e., citations to the papers published in the same country as the authors') and foreign citations (i.e., citations to the papers published in different countries), and calculate gender imbalance separately for domestic and foreign citations for each country.
It turns out that patterns of the over/under-citations for the foreign citations are qualitatively the same as those for the overall citations (see Fig. 5 and Supplementary Fig. S3).This result is expected because the foreign citations are yet dominant in China, Japan, and South Korea; they account for 98.2% of the overall citations in China, 77.8% in Japan, and 93.4% in South Korea.We now turn to domestic citations made by the papers from China, Japan, and South Korea.First, while the papers from China under-cite WW papers on average (see Fig. 5(a)), they over-cite WW papers from China (see Supplementary Fig. S2(a)).Second, papers in any gender category and any country are more likely to cite WW papers from the same country than they cite WW papers from any country, except for MM papers from Japan (see Figs. 5(b)-(e) and Supplementary Figs.S2(b)-(e)).Third, WW papers from each country are more likely to cite papers involving female authors in a prominent position (i.e., MW, WM, or WW papers) in the same country than they cite those in any country (see Fig. 5(e) and Supplementary Fig. S2(e)).In fact, on average, the WW papers from China, Japan, and South Korea over-cite the MW, WM, or WW papers from the same country at least twice more than they over-cite the MW, WM, or WW papers in general.In particular, the WW papers from Japan and South Korea over-cite the WW papers from the same country 56.8 and 35.8 times, respectively, more than they over-cite WW papers in general.These results are also consistent with the previous findings that authors tend to cite papers from the same country 13,14,17 and that the author's gender and another variable (e.g., authors' race and country) can have combined effects on gender imbalance in citation behavior 34,66 .

Discussion
In this study, we hypothesized that China, Japan, and South Korea are exposed to larger gender imbalance in academia than other countries.Therefore, we compared gender imbalance among authors in the four country groups (i.e., China, Japan, South Korea, and the other countries).We found that the fractions of female authors in China, Japan, and South Korea are smaller than that in the other countries.We also found that the gender imbalance in research career is notably larger in Japan and is present but weaker in China and South Korea than in the other countries.In terms of citation practice, papers from the three East Asian countries are more likely to under-cite WW papers (i.e., papers in which women occupy the prominent author positions) than those in the other countries do.These results are largely consistent with the previous results in that Asian countries tend to be exposed to larger gender imbalance in academia than other countries 3,15,19,21,29,37,44,58 .Because East Asia accounts for a substantial fraction of research expenditure, number of researchers, and research output in the world, gender imbalance in academia in East Asia is considered to affect our understanding of the global landscape of gender imbalance in academia.
We also hypothesized that Japan is exposed to larger gender imbalance in academia than China and South Korea.We compared the gender imbalance among authors in China, Japan, and South Korea aided by a unified and high-accuracy gender assignment method.In our data set, the fraction of female authors was the largest in China and smallest in South Korea; in previous studies, it was the largest in China 19,29,37,44 and the smallest in Japan 29,37 or South Korea 19,44 .Therefore, our results are roughly consistent with theirs.We also found that the gender imbalance in research career and the degree of under-citation of any WW papers are larger in Japan than in China and South Korea.Haghani et al. suggested that gender imbalance in total productivity has been larger in Japan than in South Korea between 2006 and 2020 27 , which is consistent with our results.Due to a poor accuracy at identifying the gender from East Asian names, other studies either failed to sample a sufficient number of gender-assigned researchers in the three East Asian countries or excluded those researchers in an early stage of their analysis 3,15,30 .In contrast, we overcame this technical barrier to comprehensively compare gender imbalance in the academia of three East Asian countries in terms of the research career and citation practice of individual researchers.Our results are a significant addition to the previous studies that examined the three countries but only in terms of the number of researchers.
For bibliographic data analysis involving gender comparison, one usually needs to identify authors' gender from their names 30,37,62 .This task is difficult for East Asian names 15,31,52 .We built an algorithm to detect the gender of Chinese, Japanese, and Korean names with a classification accuracy of at least 90% on our benchmark data.In the course of parameter tuning, we found that, given the parameter values, the classification accuracy depends on the era, which is quantified by the year of the first publication, as well as the country.For example, for the authors in China, we needed to impose a higher threshold of 'accuracy', θ , when the names of more recent than old authors are input.This phenomenon implies that the gender of more recent Chinese names is more difficult to detect.In contrast, it was more difficult to detect the gender of older than more recent authors in Japan.We also observed that tuning the threshold on the number of samples in the database, n s , can improve the accuracy of gender inference for East Asian names; other studies used the same technique before for author names from various countries 44,57 .Despite our efforts, the fraction of gender-assigned authors in China (i.e., 5.0%) was much lower than that in Japan and South Korea (i.e., 60.3% and 43.7%, respectively).Therefore, our Chinese data may not be representative of the entire population of Chinese researchers.It is notably difficult to infer gender from Chinese names written in English 3,15,32 .As in the case studies for other countries 12,36 , investigating gender imbalance in Chinese academia using data with names and other information in the Chinese language warrants future work.
Our study has additional limitations.First, when analyzing the research career, we focused on the authors whose last publication year was 2015 or earlier.Therefore, our data set may not reflect recent efforts to support the academic participation of women in East Asian countries (e.g.,China 42 , Japan 1 , and South Korea 7 ).Second, we only used the OpenAlex database.Because OpenAlex is a successor of MAG, our results may be biased due to the problems that the MAG had.For example, MAG database covers a larger number of publications but misses more citations than other data (e.g., Scopus and Web of Science) do 60 .Third, our analysis only focused on researchers writing academic papers.A recent study suggested that Japanese children acquire the gender stereotype to associate brilliance with males after they start to go to school 48 .It is also important to investigate gender imbalance in wider education than has been investigated in the present study (e.g., Ref. 22 ).Overcoming these and other limitations is expected to help us better quantify and improve gender imbalance in academic systems and in practices of individual researchers.
Our goal is to find a gender assignment method that yields a classification accuracy of at least 90% for each gender, each country group, and each year subgroup.For each country group, we first examined six baseline methods: "Global", "Local", "Hybrid", "Globalα", "Localα", and "Hybridα".In the Global method, for each author, we feed each candidate of their first name to the API without specifying their country.Then, among the API's outputs, we kept only the outputs for which the 'accuracy' that the API returns is at least θ and the number of samples is at least n s .We set θ = 90% and n s = 1.We then find the largest 'accuracy' value among all the input first-name candidates that return female as output.Similarly, we find the largest 'accuracy' value among all the input first-name candidates that return male as output.If the former is larger than the latter, we assign female to the author.If the former is smaller than the latter, we assign male to the author.If the former is equal to the latter, then we do not assign any gender to the author.
The only difference between the Global, Local, and Hybrid methods is the inputs to the API.In the Local method, for each author, we feed each candidate of their first name to the API but not their country.In the Hybrid method, for each author, we feed each candidate of their first name to the API without specifying their country, and then we again feed the same first name to the API by specifying their country.Moreover, we define the Globalα, Localα, and Hybridα methods by changing n s = 1 to n s = 10 in the Global, Local, and Hybrid methods, respectively.Raising n s may improve the classification accuracy; the same technique was used before 2,3 .The method with the best classification accuracy among the six baseline methods does not reach 90% classification accuracy for some pairs of the country group and year subgroup.In this case, we examine additional methods in which we separately adjust θ or n s just for the pairs with low classification accuracy, as we describe in the remainder of this section, until the classification accuracy reaches 90% in all the cases.

S3.2 Authors in China
We found that the Local method yields the highest classification accuracy on average over the eight subgroups (i.e., four year subgroups for each gender) among the Global, Local, and Hybrid methods (see Table S1).The Local method inferred the gender of male authors in each year subgroup with more than 90% classification accuracy.However, the classification accuracy for the females with the same method was much lower than 90%.Then, we additionally considered Globalα, Localα, and Hybridα.These variants improve the classification accuracy, and Localα yields the highest average of the classification accuracy over the eight subgroups (see Table S1).However, the classification accuracy of Localα is still much lower than 90% for the females whose first publication year is 1991 or later.
Therefore, we considered three additional variants of Localα, named Localβ , Localγ, and Localδ .Localβ is the same as Localα except that, in Localβ , we set θ = 95% for the authors whose first publication year is 1991 or later.Then, the classification accuracy for the females whose first publication year is 2011 or later is higher than 90%; however, that for the females whose first publication year is between 1991 and 2010 is not (see Table S1).Next, we considered Localγ, which is the same as Localβ except that Localγ uses θ = 99% for the authors whose first publication year is between 1991 and 2010.With Localγ, the classification accuracy for the females whose first publication year is between 1991 and 2000 is higher than 90%; however, that for the females whose first publication year is between 2001 and 2010 is not (see Table S1).Therefore, we considered Localδ , which is the same as Localγ except that Localδ uses n s = 50 for the females whose first publication year is between 2001 and 2010.Then, the classification accuracy for the females whose first publication year is between 2001 and 2010 is higher than 90% (see Table S1).Therefore, we used Localδ , which yields at least 90% classification accuracy for the females and males in each year subgroup.

S3.3 Authors in Japan
For the authors in Japan, Localα yielded the highest average of the classification accuracy over the eight subgroups among the six baseline methods.Localα detected the gender of the males in each year subgroup and of the females whose first publication year is 1991 or later with more than 90% accuracy (see Table S2).However, the classification accuracy for the females whose first publication year is 1990 or before is much smaller than 90% with Localα.
Therefore, we considered two additional variants of Localα, named Localε and Localζ .In Localε, we changed Localα by setting θ = 95% just for the authors whose first publication year is 1990 or before.We found that, with Localε, the classification accuracy for the females whose first publication year is 1990 or before is still lower than 90% (see Table S2).In Localζ , we changed Localε by setting θ = 99% just for the authors whose first publication year is 1990 or before.The classification accuracy with Localζ is higher than 90% for the females whose first publication year is 1990 or before (see Table S2).Therefore, we used Localζ , which yields at least 90% classification accuracy for the females and males in each year subgroup.

S3.4 Authors in South Korea
For the authors in South Korea, Localα yielded the highest average of the classification accuracy over the eight subgroups among the six baseline methods, which was higher than 90% for the females and males in each year subgroup (see Table S3).Therefore, we used Localα.17/25

S3.5 Authors in the other countries
For the authors in the other countries, Global and Globalα yielded the highest average of the classification accuracy over the eight subgroups among the six baseline methods.Both methods yielded an classification accuracy higher than 90% for the females and males in each subgroup (see Table S4).Note that Globalα yielded exactly the same classification accuracy for the females and males in each subgroup as Global because all the 200 sampled authors have first names that have more than ten samples in the database.As we did for the authors in China, Japan, and South Korea, and as previous studies also did 2,3 , we decided to use Globalα for the authors in the other countries.

S4 Citation count and its normalization
We count and normalize the number of citations that each paper has received using the method proposed in Ref. 1 as follows.
For each paper z, we first count the number of citations received by z within 10 years after its publication without self-citations (i.e., citations to the papers whose authors overlap those of z).Then, we define the citation impact of z as the number of citations divided by the average number of citations received by the papers published in the same year.

S5 Fraction of female authors by research discipline
Table S5 shows the number of gender-assigned authors and the fraction of female authors in China, Japan, South Korea, and the other countries by author's research discipline.

S6 Matching experiments for the papers in which the authors occupy the prominent position
Figure S1 shows the results for the matching experiments in which we restrict the analysis to the papers in which the authors occupy the prominent author position.

S7 Correlation between author's career length and number of coauthors
Table S6 shows the Pearson correlation coefficients between the career length and the number of coauthors for the set of all the authors, that of female authors, and that of male authors in each country group.

S8 Gender imbalance in domestic and foreign citations
Figure S2 shows the over/under-citations for domestic citations made by papers from China, Japan, and South Korea.Figure S3 shows the corresponding results for foreign citations.
Table S1.Classification accuracy of the different gender assignment methods for the authors in China.In each cell, we report the classification accuracy for female and male authors in red and blue, respectively.The number after the classification accuracy shows the number of authors among the 25 selected authors for whom we were able to manually assign the binary gender.

Figure 1 .
Figure 1.Counts of authors in China, Japan, South Korea, and the other countries.(a) Number of authors between 1990 and 2020.(b) Fraction of female authors between 1990 and 2020.

Figure 2 .Figure 3 .
Figure 2. Gender imbalance in the research career for the authors in China, Japan, South Korea, and the other countries.(a) Total productivity.(b) Total impact.(c) Annual productivity.(d) Career length.In each panel, the gender gap for all authors in the country group, top 20%, middle 20%, and bottom 20% authors are shown.For example, the top 20% refers to the gender gap between the top 20% females and the top 20% males in the country group.

Figure 4 .
Figure 4. Gender imbalance in research performance after controlling for the career length or the number of coauthors.(a) Total productivity.(b) Total impact.Each panel shows the results of the matching experiment in which the author's career length (CL) and/or their number of coauthors (NC) are controlled in addition to their country group, year of the first publication, and research discipline.The bar labeled "No control" in each panel is identical to that labeled "Overall" for the corresponding indicator and country group in Fig. 2.
(a)).Our results for China

Table S2 .
Classification accuracy of the different gender assignment methods for the authors in Japan.

Table S3 .
Classification accuracy of the different gender assignment methods for the authors in South Korea.

Table S4 .
Classification accuracy of the different gender assignment methods for the authors in the other countries.